Cook the spaghetti according to package instructions until al dente. Before draining, reserve 1/2 cup of the pasta cooking water, then drain the pasta and set aside.
Open the 6 oz can of tuna and drain the oil. Transfer the tuna to a bowl and break it into flakes with a fork; set aside.
In a cold sauté pan add the 3 tbsp olive oil, the minced garlic, and the 1/4 tsp red pepper flakes. Place the pan over medium heat and warm gently, stirring occasionally, until the garlic is fragrant and just begins to sizzle (about 30–60 seconds). Avoid letting the garlic brown.
Add the 2 tbsp capers, the lemon zest, the 2 tbsp lemon juice, the 1/2 tsp kosher salt, and the 2 tbsp chopped parsley to the pan. Cook, stirring, for about 2 minutes so the flavors combine.
Remove the pan from the heat and add the flaked tuna. Stir gently to coat the tuna with the sauce, keeping some larger pieces intact.
Add the drained spaghetti to the pan and toss to combine. If the mixture seems dry, add reserved pasta water 1–2 tablespoons at a time until the sauce coats the pasta evenly.
Taste and adjust seasoning if needed. Serve immediately.